Shortly after the polls closed Tuesday in Texas' first-in-the-nation primary, Cruz tweeted a 60-second country jingle targeting his Democratic challenger, U.S. Rep. Beto O'Rourke of El Paso. The jingle calls O'Rourke "liberal Robert" and says he "changed his name to Beto."

O'Rourke responded Wednesday with his own tweet : a childhood photo of him wearing a shirt inscribed "BETO" in block letters.

Cruz said in the interview Wednesday that "some of it is just to have a sense of humor." After saying his full name, Cruz told the story of his father, who immigrated to the United States from Cuba.

Mark Jones, a Rice University political scientist, said one implied motive might be to remind Texas voters that O'Rourke isn't of Latino descent.

While Democratic primary turnout surged past 1 million on Tuesday, it was still well short of the more than 1.5 million people who voted in the Republican primary. Despite having fundraising success and drawing national attention, O'Rourke enters the general election against Cruz as a heavy underdog.

Any Democrat hoping to win statewide in Texas and break a 24-year losing streak for the state party will have to draw lots of Latino voters to the polls.

While O'Rourke is of Irish descent, he speaks Spanish and represents a majority Latino district in El Paso, a far West Texas city that borders Mexico. Cruz admitted in a 2012 interview that his Spanish was "lousy."

"So many people in Texas, because of his first name, sometimes assume that he's Latino," Jones said of O'Rourke. "This is one way for Cruz to indirectly signal that he's not."

"His best option going against O'Rourke is to lower O'Rourke's likability among Texans so that they view them in an equal manner," Jones added.

Asked in a separate CNN interview if he would respond with his own song, O'Rourke declined.

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"I just don't think that's what folks in Texas want us to focus on," he said. "We can get into name-calling and talk about why the other person is such an awful guy, or we can focus on the big things that we want to do for the future of our country."